XOR gate

XOR gate (sometimes EOR, or EXOR and pronounced as Exclusive OR) is a digital logic gate that gives a true (1 or HIGH) output when the number of true inputs is odd. An XOR gate implements an exclusive or (${\displaystyle \nleftrightarrow }$) from mathematical logic; that is, a true output results if one, and only one, of the inputs to the gate is true. If both inputs are false (0/LOW) or both are true, a false output results. XOR represents the inequality function, i.e., the output is true if the inputs are not alike otherwise the output is false. A way to remember XOR is "must have one or the other but not both".

An XOR gate may serve as a "programmable inverter" in which one input determines whether to invert the other input, or to simply pass it along with no change. Hence it functions as a inverter (a NOT gate) which may be activated or deactivated by a switch.^[1][2]

XOR can also be viewed as addition modulo 2. As a result, XOR gates are used to implement binary addition in computers. A half adder consists of an XOR gate and an AND gate. The gate is also used in subtractors and comparators.^[3]

The algebraic expressions ${\displaystyle A\cdot {\overline {B}}+{\overline {A}}\cdot B}$ or ${\displaystyle (A+B)\cdot ({\overline {A}}+{\overline {B}})}$ or ${\displaystyle (A+B)\cdot {\overline {(A\cdot B)}}}$ or ${\displaystyle A\oplus B}$ all represent the XOR gate with inputs A and B. The behavior of XOR is summarized in the truth table shown on the right.